When the AI singularity takes over, what will there be left for us to do?
Given all your assumptions about AI turn out to be true, we would have some kind of utopia, where no one has to work, and there is plenty of everything. Fair enough. Your other assumptions is about human nature, and that is where I'd challenge your conclusion: Just because there are computers better than humans at some task, that does not automatically take all enjoyment from doing it.

I have three arguments in favor of my stance.


There already are computers better than humans at checkers, chess, backgammon, starcraft, mastermind, go,.. and many more. Yet these games still get played, even if no human can hope to ever be as good as a computer.
There will be domains where the evaluation of quality is so vague or personal, that the notion of being "better" is useless in any objective sense. I am thinking mainly about art. Playing into argument one, photo cameras are already better "painters" of reality than humans can ever hope to be, yet people still paint. And their paintings gets appreciated, even the photo-realistic kind.
I'd say that the whole mindset of "if someone is better than me at x it is not worth doing x" will have outlived its lifetime very shortly. Society didn't always spin that way I feel, it is largely due to the influence of the North American way of life to always strive to be #1 and everything below that being trash. Globalization already puts this way of thinking at risk, with many young people being disillusioned or even depressed because, flippantly put, "whatever you do, there is always an Asian kid who does it 10 times better". We don't have to wait for AI to outshine us, the rest of the world already does. As a consequence, we need to adapt our way of approaching that fact, stop seeing it as diminishing to our worth, and move on.


As a closing note, I also see it as a problem to the general population that within a short time we essentially have to change a very substantial part of our world view, AI being better than us, us not having to work anymore etc. All the economical revolutions in the past, the neolithic, the industrial, and most recently, the digital, had a longer transitional period where people could grow accustomed to the new world. And even with that transition it was hard enough for many people. Yet, most dealt with it, and later generations can hardly imagine a world where the new change doesn't exist yet, and I personally don't see why the next revolution should be any different.